Parabola

Question 1

What is the standard equation of the parabola ?

Answer 1

y^=4ax

Question 2

What is latus rectum of a parabola ?

Answer 2

Latus rectum of a parabola is a special type of double ordinate which passes through the foci. Focus of parabola is midpoint of latus rectum

Question 3

On parabola , what is the perpendicular distance of focus to directrix equal to ?

Answer 3

Half the directrix.

Question 4

In parabola , what is the vertex of parabola ?

Answer 4

Vertex of parabola is the middle point of the focus and point of intersection of directrix and axis.

Question 5

When are two parabolas considered equal ?

Answer 5

Two parabolas are considered equal when they have the same latus rectum.

Question 6

What is the coordinate of the foci of curve y^=4ax ?

Answer 6

(a,0)

Question 7

What is the equation of directrix of curve y^=4ax

Answer 7

x=-a

Question 8

What is the equation of axis of the curve y^= 4ax

Answer 8

y=0

Question 9

What are the parametric coordinate of parabola of equation y^=4ax

Answer 9

Any point on parabola y^=4ax is (at^, 2at), it is referred as point t. T is parameter , it varies from point to point.

Question 10

What is the minimum length of focal chord ?

Answer 10

Minimum length of focal chord is 4a ie length of latus rectum.

Question 11

What is focal distance of a point on the parabola ?

Answer 11

Focal distance is the distance between point P on parabola and focus S, ie PS. It’s equal to a+x

Question 12

What is the tangent at a point (x1,y1) lying on the parabola ?

Answer 12

yy1= 2a(x+x1)

Question 13

What is the slope form of tangent to parabola ?

Answer 13

y= mx + a/m

Point or contact is [(a/m^),(2a/m)]

Question 14

What is the director circle of parabola ?

Answer 14

Director circle of parabola is x + a= 0 ie parabolas own directrix.

Question 15

What is the normal at point (x1,y1) on the parabola ?

Answer 15

Slope of normal is -y1/2a.
Also it passes through (x1,y1)
It’s eq y-y1=-y1/2a(x-x1)

Question 16

What is the normal of parabola in slope form ?

Answer 16

If m is the slope of normal , then it’s equation is y=mx - 2am -am^3. It will cut the parabola at point (am^,-2am)

Question 17

What can you say about semi latus rectum of the parabola y^=4ax?

Answer 17

Semi latus rectum is the harmonic mean between the segments of any focal chord of the parabola.

Question 18

What is the coordinates of the orthocentre of the triangle formed by three tangents of the parabola y^=4x?

Answer 18

It lies on the directrix and had coordinates

-a,a(t1+t2+t1t2t3)

Question 19

What is the shortest normal chord of any parabola with latus rectum =4a?

Answer 19

6a√3